1. March 6th, 2006CALICE meeting, UCL1 Position and angular resolution studies with ECAL TB prototype Introduction Linear fit method Results with 1, 2, 3, and 5 GeV electrons conclusions Anne-Marie Magnan, IC London.

2. March 6th, 2006CALICE meeting, UCL2 Introduction oComplete test beam prototype : 30 layers, 1 cm 2 cells, 9 wafers per layer. oObjective : determine position and angular resolution in test beam data, compared with the one obtained in MC simulation. oMethod : linear fit  take into account correlations between layers. oFor this study, only 1, 2, 3 and 5 GeV single electrons (DESY test beam). oOwn generation with Mokka05.05. Beam position and RMS : (0 ±10, 0 ± 10, -220 ± 0) (in mm). Current LCIO output does not allow to have the “truth” position in 1 st ECAL layer after scattering in air/trackers materials.

3. March 6th, 2006CALICE meeting, UCL3 Linear fit method : definition of variables oDefinition of x and y position per layer : i = hits in layer L. z Vz=-220 mm x,y * V x, V y -197.6, 1 st Si layer x MC,y MC Variable of interest : reconstructed position compared to the expected one :  Dx = x – x MC, Dy = y – y MC , _ _ For this simulation : Redefine z = 0  1 st Si layer Layer

4. March 6th, 2006CALICE meeting, UCL4 Linear fit method : definition of the χ 2 oEstimator of how accurate the prediction of the measurement is : Without correlations between variables : With correlations between variables : W ij is the inverse of the error matrix E ij : i,j = 1,.....,30 for x 31,.....,60 for y = 0

5. March 6th, 2006CALICE meeting, UCL5 Error matrix (= covariance matrix)  Error matrix normalized on the diagonal values (= correlation matrix)  Linear fit method : error matrix oW ij is calculated thanks to the whole sample (25,000 electrons) x y x y x y x y No significant correlations between x and y 1 GeV Funny pattern : due to non- overlapping layers in x ??? Layer Diagonal terms

6. March 6th, 2006CALICE meeting, UCL6 Error matrix for higher energies 2 GeV 3 GeV 5 GeV

7. March 6th, 2006CALICE meeting, UCL7 Linear fit method : minimisation of the χ 2 oX and y are uncorrelated : we consider 2 (30,30) matrices  2 independent fits : one for x, the other for y.  we can then look for the parameters (p 0x,p 1x ) of the linear fit which minimize the χ 2 : x = x or y Reminder : = o This gives the following equation :

8. March 6th, 2006CALICE meeting, UCL8 Linear fit method : expected resolution σ p0x (mm) σ p0y (mm) σ p1x (mrad) σ p1y (mrad) 1 GeV2.42.85860 2 GeV2.42.84850 3 GeV2.32.74144 5 GeV2.22.53537 z -220 mm x,y * -197.6, 1 st Si layer p0 p1 σ p0 σ p1 o Angular resolution decrease when E increase : more layers on the back  better constraints o Position resolution decrease as well when E increase : more hits  better estimate of the average position o Position resolution is higher in y, why ??????? Best case : if all layers !!+ tracker resolution!! !! in data !! Best case : if all layers

9. March 6th, 2006CALICE meeting, UCL9 Position and angular resolution obtained on an event by event basis o  Therefore have to solve it event by event. To solve this, need to take into account only layers i and j with hits  remove layers with no hit from error matrix, then invert to have W matrix. Equation to solve :

10. March 6th, 2006CALICE meeting, UCL10 Results event by event for parameter resolution matrices =

11. March 6th, 2006CALICE meeting, UCL11 Result event by event for (p 0 – p 0MC ) x,y x y Energy σ p 0x (mm) if all layers σ p 0y (mm) if all layers 1 GeV2.6 2.43.1 2.8 2 GeV2.5 2.42.9 2.8 3 GeV2.4 2.32.8 2.7 5 GeV2.2 2.6 2.5

12. March 6th, 2006CALICE meeting, UCL12 Result event by event for (p 1 – p 1MC ) x,y x y Energy σ p 1x (mrad) if all layers σ p 1y (mrad) if all layers 1 GeV71 5874 60 2 GeV54 4856 50 3 GeV45 4148 44 5 GeV36 3539 37

13. March 6th, 2006CALICE meeting, UCL13 Consistency checks oPull of the distributions for Δp 0 (=p 0 – p 0MC ) and Δ p 1 0.88-0.96 0.96-0.99 0.95-0.97 0.97-0.98

14. March 6th, 2006CALICE meeting, UCL14 With material in front of ECAL oBeam position : (4,7,10000) mm oExpected effect of air scattering in 10 m  ~ 13 mm spread. oObserved : ~ 16 mm spread. oExpected resolution : The “true” position is now given by hits in last DC layer σ p0x = 5.2 mm, σ p0y = 5.3 mm σ p1x = 70 mrad, σ p1y = 69 mrad  still correlations. Need to have the “true” position of MC particle at front ECAL face. 1 GeV

15. March 6th, 2006CALICE meeting, UCL15 Future work oStudy with missing layers : better to have front, middle, back ? First layers needed for position resolution, and last ones for angular resolution… but depend on energy. Hakan + AM o Redo everything with material in front, and truth entry point. o Study of reconstructed tracking resolution to separate the 2 sources and allow to compare with data. o Redo everything when realistic digitisation is available.

16. March 6th, 2006CALICE meeting, UCL16 Thank you for your attention